Relations and Functions: Rationals, Logs and Exponentials

Rational expressions and equations, the laws of logarithms and exponential models. The heaviest weighted section of the Mathematics 30-2 diploma.

15 questions, free, marked as you go with a worked explanation on every one.

What this covers

For the rational expression (x + 3) / (x² - 4), what are the non-permissible values of x?
Solve for x: 12/x + 3 = 7. Give the value of x.
Evaluate log₂ 32.
Solve for x: 3^(x + 1) = 81.
Use the laws of logarithms to evaluate log 1000 - log 10.
A medical isotope has a half-life of 8 hours. A hospital receives a 200 mg sample. How many milligrams of the isotope remain 24 hours after it arrives?
A town's population is 5 000 and is growing at a steady 4% per year. To the nearest tenth of a year, how long will it take for the population to double?
The depth of water at a harbour is modelled by d = 3 sin(30t)° + 5, where d is the depth in metres and t is the time in hours after midnight. What is the greatest depth of water at the harbour, in metres?
A radioactive sample decays with a half-life of 5 years. After how many years will only one eighth of the original sample remain?
Evaluate log base 3 of 27.
Solve for x: log(x) = 2 (base 10).
Given that log(5) is approximately 0.699, find log(5^3), to the nearest hundredth.
Solve for x: sqrt(x + 7) = 4.
Solve for x: 2^(x - 1) = 16.
Solve for x: 6 / (x - 2) = 3.